Does the point (-5, -1, -5)lie on any of the level surfaces of $f ( x , y , z ) = x ^ { 2 } + 4 y ^ { 2 } + z ^ { 2 }$ ? If so, what is the equation of that level surface?

Question

Quizplus · Accepted Answer

Substituting the point (-5, -1, -5) into the function $f(x, y, z) = x^2 + 4y^2 + z^2$ gives $f(-5, -1, -5) = (-5)^2 + 4(-1)^2 + (-5)^2 = 25 + 4 + 25 = 54$. Therefore, the point lies on the level surface defined by $x^2 + 4y^2 + z^2 = 54$.

Does the Point (-5, -1, -5)lie on Any of the Level